Suppose that X is a random variable for which the moment generating function is as follows: MX(t) = e^(2t^2+3t) for −∞ < t < ∞. Find the mean and variance of X. (b) Suppose that X has moment generating function MX(t) =(3e^t/4 + 1/4)^6 (i) Find the p.m.f. of X.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose that X is a random variable for which the moment generating
MX(t) = e^(2t^2+3t) for −∞ < t < ∞.
Find the mean and variance of X.
(b) Suppose that X has moment generating function MX(t) =(3e^t/4 + 1/4)^6
(i) Find the p.m.f. of X.
(ii) Find the mean and variance of X.
(c) A person with some finite number of keys wants to open a door. He tries the keys one-by-one independently at random with replacement. How many trails you expect, from him, to open the door?
(d) Obtain the form of moment generating function (m.g.f.) for the following p.m.f. –
p(x) = ((2^x)(e^-2))/×!, x = 0,1,2, … .
Also calculate the mean and variance from m.g.f.
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